A131320 2*n - maximal value arising in the sequence S(n) representing the digital sum analog base n of the Fibonacci recurrence.

1, 2, 3, 3, 5, 3, 3, 3, 5, 3, 3, 11, 7, 3, 3, 6, 9, 3, 3, 8, 9, 10, 11, 3, 9, 3, 3, 3, 15, 26, 8, 13, 10, 12, 3, 11, 19, 3, 23, 13, 13, 3, 21, 3, 23, 10, 3, 3, 9, 3, 3, 16, 17, 3, 3, 23, 17, 19, 29, 22, 11, 3, 17, 10, 25, 3, 22, 3, 35, 30, 11, 29, 57, 3, 3, 17, 65, 16, 13, 20, 21, 3, 3

Offset: 1

Author

Hieronymus Fischer, Jul 08 2007

Keywords

• nonn
• base

Comments

The inequality a(n)>=3 holds for n>2.

a(n)=3 arises infinitely often; lim inf a(n)=3 for n-->oo.

Examples

			a(3)=3, since the digital sum analog base 3 of the Fibonacci sequence is 0,1,1,2,3,3,2,3,3,... where the pattern {2,3,3} is the periodic part (see A131294) and so has a maximal value of 3 which implies 2*3-3=3. a(9)=5, because the pattern here is {2,3,5,8,13,13,10,7,9,8,9,9} (see A010076) where the maximal value is 13 and so 2*9-13=5.
		

Crossrefs

Cf. A000032, A000045, A000032, A131318, A131320.

See A010074, A010075, A010076, A010077, A131294, A131295, A131296, A131297 for the definition of the digital sum analog of the Fibonacci sequence (in different bases).

Formula

a(n)=2n-A131319(n).

a(Lucas(2n))=3 where Lucas(n)=A000032(n).